Newton-Raphson
clear
clc
cd=.25;
v=36;
t=4;
g=9.81;
m=50;
Error(1)=0;
for i=1:6
f(i)=sqrt((g*m(i))/cd)*tanh(sqrt(g*cd/m(i))*t)-v;
df(i)=(1/2)*(sqrt(g/(m(i)*cd)))*tanh(sqrt((g*cd)/m(i))*t)-(g*t/(2*m(i)))*(sech(sqrt((g*cd)/m(i))*t)^2);
m(i+1)=m(i)-(f(i)/df(i));
Error(i+1)=abs((m(i)-m(i+1))/m(i)*100);
end
disp( ' m Error %')
disp([m',Error'])
m Error %
50.0000 0
88.3993 76.7986
124.0897 40.3741
140.5417 13.2582
142.7072 1.5408
142.7376 0.0213
142.7376 0.0000
Point Iteration
clear
clc
format short
x=linspace(0,1,9);
xi(1)=0;
Error(1)=0;
Iteration(1)=0;
for i=1:10
x(i+1)=exp(-x(i));
Error(i+1)=abs((x(i+1)-x(i))/x(i+1))*100;
Iteration(i+1)=i;
end
disp('Iteration x
Error')
disp([Iteration',x',Error'])
Iteration
x Error
0 0 0
1.0000 1.0000 100.0000
2.0000 0.3679 171.8282
3.0000 0.6922 46.8536
4.0000 0.5005 38.3091
5.0000 0.6062 17.4468
6.0000 0.5454 11.1566
7.0000 0.5796 5.9034
8.0000 0.5601 3.4809
9.0000 0.5711 1.9308
10.0000 0.5649 1.1089
>>